182edo: Difference between revisions

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'''182edo''' is the [[EDO|equal division of the octave]] into 182 parts of 6.5934 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 11-limit: <182 288 423 511 630| (patent val), <182 289 423 511 630| (182b), and <182 288 422 511 629| (182ce). Using the patent val, it tempers out the tenfold green comma, 10077696/9765625 and 3486784401/3355443200 in the 5-limit; 126/125, 1728/1715, and 1937102445/1879048192 in the 7-limit; 2187/2156, 2835/2816, 5632/5625, and 14700/14641 in the 11-limit; 364/363, 676/675, 1287/1280, and 1701/1690 in the 13-limit. Using the 182b val, it tempers out the [[Diaschismic family|diaschisma]], 2048/2025 and |-4 -37 27> in the 5-limit; 245/243, 6144/6125, and 9882516/9765625 in the 7-limit; 3025/3024, 3773/3750, and 4000/3993 in the 11-limit. Using the 182bf val, 196/195, 325/324, 364/363, and 1001/1000 are tempered out in the 13-limit. Using the 182ce val, it tempers out the [[Kleismic family|kleisma]], 15625/15552 and the double large green comma, 43046721/41943040 in the 5-limit; 2430/2401, 33075/32768, and 78125/76832 in the 7-limit; 243/242, 385/384, 2420/2401, and 6250/6237 in the 11-limit; 351/350, 1188/1183, 1287/1280, 1575/1573, and 1625/1617 in the 13-limit. Using the 182f val, 144/143, 847/845, 1001/1000, and 1716/1715 are tempered out in the 13-limit.

[[~~Category~~:~~Edo~~]]

182edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with three mappings suitable for the 11-limit: {{val| 182 288 423 511 630 }} ([[patent val]]), {{val| 182 289 423 511 630 }} (182b), and {{val| 182 288 422 511 629 }} (182ce). It does have a potential as a 2.9.15.7.17.19 [[subgroup]] temperament.

Using the patent val, it tempers out the mynic comma, 10077696/9765625 and {{monzo| -27 20 -2 }} in the 5-limit; [[126/125]], [[1728/1715]], and {{monzo| -28 18 1 -1 }} in the 7-limit; 2187/2156, 2835/2816, [[5632/5625]], and 14700/14641 in the 11-limit; [[364/363]], [[676/675]], [[1287/1280]], and 1701/1690 in the 13-limit. Using the 182f val, [[144/143]], [[847/845]], [[1001/1000]], and [[1716/1715]] are tempered out in the 13-limit.

Using the 182ce val, it tempers out the kleisma, [[15625/15552]] and the [[python comma]], 43046721/41943040 in the 5-limit; [[2430/2401]], 33075/32768, and 78125/76832 in the 7-limit; [[243/242]], [[385/384]], 2420/2401, and [[6250/6237]] in the 11-limit; [[351/350]], [[1188/1183]], 1287/1280, [[1575/1573]], and 1625/1617 in the 13-limit.

Using the 182b val, it tempers out the diaschisma, [[2048/2025]] and {{monzo| -4 -37 27 }}; in the 5-limit; [[245/243]], [[6144/6125]], and 9882516/9765625 in the 7-limit; [[3025/3024]], 3773/3750, and [[4000/3993]] in the 11-limit. Using the 182bf val, [[196/195]], [[325/324]], 364/363, and 1001/1000 are tempered out in the 13-limit. The 182bef val supports the [[shrutar]] temperament in the 19-limit and [[petrtri]] in the 2.11/5.13/5 subgroup.

=== Odd harmonics ===

=== Octave stretch ===

182edo’s approximations of 3/1, 5/1, 7/1 and 13/1 are all improved by the [[Gallery of arithmetic pitch sequences#APS of tinas|Argentina scale]] (APS47tina), a [[Octave stretch|stretched-octave]] version of 182edo. The trade-off is a slightly worse 2/1 and 11/1.

There are also several nearby [[Zeta peak index]] (ZPI) tunings which can be used for this same purpose: 1199zpi, 1200zpi, 1201zpi, 1202zpi, 1203zpi, 1204zpi and 1205zpi.

The details of each of those ZPI tunings are visible in [[User:Contribution]]’s gallery of [[User:Contribution/Gallery of Zeta Peak Indexes (1 - 10 000)|Zeta Peak Indexes (1 - 10 000)]]. Warning: due to its length, that page may slow down your device while it is open. The effect will go away after you close the page.

=== Subsets and supersets ===

Since 182 factors into {{factorization|182}}, 182edo has subset edos {{EDOs| 2, 7, 13, 14, 26, and 91 }}.

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-'''182edo''' is the [[EDO|equal division of the octave]] into 182 parts of 6.5934 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 11-limit: &lt;182 288 423 511 630| (patent val), &lt;182 289 423 511 630| (182b), and &lt;182 288 422 511 629| (182ce). Using the patent val, it tempers out the tenfold green comma, 10077696/9765625 and 3486784401/3355443200 in the 5-limit; 126/125, 1728/1715, and 1937102445/1879048192 in the 7-limit; 2187/2156, 2835/2816, 5632/5625, and 14700/14641 in the 11-limit; 364/363, 676/675, 1287/1280, and 1701/1690 in the 13-limit. Using the 182b val, it tempers out the [[Diaschismic family|diaschisma]], 2048/2025 and |-4 -37 27&gt; in the 5-limit; 245/243, 6144/6125, and 9882516/9765625 in the 7-limit; 3025/3024, 3773/3750, and 4000/3993 in the 11-limit. Using the 182bf val, 196/195, 325/324, 364/363, and 1001/1000 are tempered out in the 13-limit. Using the 182ce val, it tempers out the [[Kleismic family|kleisma]], 15625/15552 and the double large green comma, 43046721/41943040 in the 5-limit; 2430/2401, 33075/32768, and 78125/76832 in the 7-limit; 243/242, 385/384, 2420/2401, and 6250/6237 in the 11-limit; 351/350, 1188/1183, 1287/1280, 1575/1573, and 1625/1617 in the 13-limit. Using the 182f val, 144/143, 847/845, 1001/1000, and 1716/1715 are tempered out in the 13-limit.
+{{Infobox ET}}
+{{ED intro}}
-[[Category:Edo]]
+edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with three mappings suitable for the 11-limit: {{val| 182 288 423 511 630 }} ([[patent val]]), {{val| 182 289 423 511 630 }} (182b), and {{val| 182 288 422 511 629 }} (182ce). It does have a potential as a 2.9.15.7.17.19 [[subgroup]] temperament.
+Using the patent val, it tempers out the mynic comma, 10077696/9765625 and {{monzo| -27 20 -2 }} in the 5-limit; [[126/125]], [[1728/1715]], and {{monzo| -28 18 1 -1 }} in the 7-limit; 2187/2156, 2835/2816, [[5632/5625]], and 14700/14641 in the 11-limit; [[364/363]], [[676/675]], [[1287/1280]], and 1701/1690 in the 13-limit. Using the 182f val, [[144/143]], [[847/845]], [[1001/1000]], and [[1716/1715]] are tempered out in the 13-limit.
+Using the 182ce val, it tempers out the kleisma, [[15625/15552]] and the [[python comma]], 43046721/41943040 in the 5-limit; [[2430/2401]], 33075/32768, and 78125/76832 in the 7-limit; [[243/242]], [[385/384]], 2420/2401, and [[6250/6237]] in the 11-limit; [[351/350]], [[1188/1183]], 1287/1280, [[1575/1573]], and 1625/1617 in the 13-limit.
+Using the 182b val, it tempers out the diaschisma, [[2048/2025]] and {{monzo| -4 -37 27 }}; in the 5-limit; [[245/243]], [[6144/6125]], and 9882516/9765625 in the 7-limit; [[3025/3024]], 3773/3750, and [[4000/3993]] in the 11-limit. Using the 182bf val, [[196/195]], [[325/324]], 364/363, and 1001/1000 are tempered out in the 13-limit. The 182bef val supports the [[shrutar]] temperament in the 19-limit and [[petrtri]] in the 2.11/5.13/5 subgroup.
+=== Odd harmonics ===
+{{Harmonics in equal|182}}
+=== Octave stretch ===
+edo’s approximations of 3/1, 5/1, 7/1 and 13/1 are all improved by the [[Gallery of arithmetic pitch sequences#APS of tinas|Argentina scale]] (APS47tina), a [[Octave stretch|stretched-octave]] version of 182edo. The trade-off is a slightly worse 2/1 and 11/1.
+There are also several nearby [[Zeta peak index]] (ZPI) tunings which can be used for this same purpose: 1199zpi, 1200zpi, 1201zpi, 1202zpi, 1203zpi, 1204zpi and 1205zpi.
+The details of each of those ZPI tunings are visible in [[User:Contribution]]’s gallery of [[User:Contribution/Gallery of Zeta Peak Indexes (1 - 10 000)|Zeta Peak Indexes (1 - 10 000)]]. Warning: due to its length, that page may slow down your device while it is open. The effect will go away after you close the page.
+=== Subsets and supersets ===
+Since 182 factors into {{factorization|182}}, 182edo has subset edos {{EDOs| 2, 7, 13, 14, 26, and 91 }}.